Home
Class 12
MATHS
A variable line passes through a fixed p...

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2,0), (0,2) and (1,1) on the line is zero. Find the coordinate of the point P.

Text Solution

Verified by Experts

Let the equation of the variable line be
ax+by+c = 0
Then according to the given condition, we get
`(2a+c)/(sqrt(a^(2) + b^(2))) + (2b+c)/(sqrt(a^(2) + b^(2))) + (-2a-2b+c)/(sqrt(a^(2)+b^(2))) = 0`
or c=0
which shows that the line passes through (0,0) for all values of a and b.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Single)|82 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Multiple)|30 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.5|8 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

Similar Questions

Explore conceptually related problems

The algebraic sum of the perpendicular distances from the points A(-2,0),B(0,2) and C(1,1) to a variable line be zero,then all such lines

If the algebraic sum of the perpendicular distances from the points (2.0)(0,2) and (4.4) to a variable line is ' ^(prime0) ' then the line passes through the fixed point

A straight line passes through a fixed point (2, 3).Locus of the foot of the perpendicular on it drawn from the origin is

If the algebraic sum of the perpendicular distances of the points (4,0),(0,4) and (2,2) form a variable straight line is zero.The line passes through a fixed point (p,q) then 3p+q=

If the algebraic sum of the perpendiculars from the points (2,0),(0,2),(1,1) to a variable line be zero,then prove that line passes through a fixed-point whose coordinates are (1,1) .

A variable straight line passes through a fixed point (h,k). Find the locus of the foot of the perpendicular on it drawn from the origin.

If the algebraic sum of the perpendiculars from the points (2,0),(0,2),(1,1) to a variable be zero,then prove that the line passes through a fixed-point whose coordinates are (1,1)

Find the equation of the perpendicular drawn from the point P(-2,3) to the line x-4y+7=0. Also, find the coordinates of the foot of the perpendicular.